Perception-based artifact quantification for volume rendering

ABSTRACT

Artifact quantification is provided in volume rendering. Since the visual conspicuity of rendering artifacts strongly influences subjective assessments of image quality, quantitative metrics that accurately correlate with human visual perception may provide consistent values over a range of imaging conditions.

RELATED APPLICATIONS

The present patent document claims the benefit of the filing date under35U.S.C. §119(e) of Provisional U.S. Patent Application Ser. No.60/864,693, filed Aug. 1, 2007, which is hereby incorporated byreference.

BACKGROUND

The present embodiments relate to volume rendering. In particular,medical data is volume rendered.

Volume rendering is a general method to composite 3D digital volumetricdata onto a 2D image. The quality and appearance of the resulting imagecan vary widely from one volume rendering engine to another due to thechoice of different tradeoffs in different implementations. Even withinone volume rendering engine, different image quality and appearance canbe produced depending on the choice of parameters. Other than grosserrors, there is often no right or wrong resulting image, only whetherthe resulting image is “better” or “worse” in revealing the desiredfeatures for a particular task or in minimizing the appearance ofundesirable rendering artifacts.

The choice of rendering engine and parameters is often left up to thesubjective heuristics of the software developers, who attempt to selectparameters that would yield good quality given rendering speedperformance considerations. A volume rendering engine is capable ofproducing a range of image qualities that are inversely related to therendering speed. Faster rendering methods often rely on simpleralgorithms and approximations that can introduce visible distortions orstructural artifacts that degrade image quality.

Common volume rendering artifacts include shading edge noise, edgenon-smoothness, striations, and opacity inconsistency. Shading noise isdark and light grains and often occurs in regions of the data where asurface is ill defined. Small noise levels in the data are exaggeratedin the shading computation. Shading noise artifacts are common amongvolume rendering engines that use gradient-based shading methods withoutspecial surface treatments. Edge non-smoothness often occurs when aslice-based volume is clipped by a binary mask in an orientation that isnot orthogonal to the volume axes. Striation artifacts may result fromvarious sources such as under-sampling, the choice of filtering kernel,quantization, or classification schemes. Opacity inconsistency occurswhen a volume renderer fails to account fully for the size variations inanisotropic volume data, resulting in variations in visible image colorand/or luminance as the volume is rotated.

The tradeoffs between quality and rendering speed are evaluated throughsubjective visual assessments by rendering engine developers.Conventional distortion metrics, such as mean squared error, havelimited utility because they often fail over a range of image andartifact characteristics. Mean squared error does not provide ameaningful quantitative reference since its value highly depends on thecontent of the image.

BRIEF SUMMARY

By way of introduction, the preferred embodiments described belowinclude methods, systems, instructions, and computer readable media forartifact quantification in volume rendering. Since the visualconspicuity of rendering artifacts strongly influences subjectiveassessments of image quality, quantitative metrics that accuratelycorrelate with human visual perception may provide consistent valuesover a range of imaging conditions.

In a first aspect, a system is provided for artifact quantification involume rendering. A memory is operable to store a dataset representing athree-dimensional volume. A processor is operable to volume render atwo-dimensional representation of the volume from the dataset and isoperable to determine a quantity representing an artifact as a functionof a perception-based visual quality metric. A display is operable todisplay the two-dimensional representation of the volume, the quantity,or both.

In a second aspect, a method is provided for artifact quantification involume rendering. A volume rendered image is volume rendered from adataset. A processor quantifies visibility to a user of an undesirablerendering feature in the volume rendered image.

In a third aspect, a computer readable storage medium has stored thereindata representing instructions executable by a programmed processor forartifact quantification in volume rendering. The storage medium includesinstructions for volume rendering an image representation of a volumefrom a data set representing the volume, calculating a first quantitywith a human visual model from the image representation, and identifyinga rendering artifact as a function of the first quantity.

The present invention is defined by the following claims, and nothing inthis section should be taken as a limitation on those claims. Furtheraspects and advantages of the invention are discussed below inconjunction with the preferred embodiments and may be later claimedindependently or in combination.

BRIEF DESCRIPTION OF THE DRAWINGS

The components and the figures are not necessarily to scale, emphasisinstead being placed upon illustrating the principles of the invention.Moreover, in the figures, like reference numerals designatecorresponding parts throughout the different views.

FIG. 1 is a block diagram of one embodiment of a system for artifactquantification in volume rendering;

FIG. 2 is a flow chart diagram of one embodiment of a method forartifact quantification in volume rendering; and

FIG. 3 shows one example of contrast sensitivity curves by luminance.

DETAILED DESCRIPTION OF THE DRAWINGS AND PRESENTLY PREFERRED EMBODIMENTS

The visibility of artifacts in volume rendered images is quantitativelyevaluated. The subjective visual quality of volume rendered images isoften influenced by the presence and severity of several commonartifacts. Conventional image difference metrics, such as mean squarederror, often fail to correlate consistently with perceived differencesor quality. Visual image quality metrics (VIQM) quantitatively measurethe visibility of volume rendering artifacts by simulating imageperception by the human visual system. VIQM allows for evaluating andoptimizing volume rendering methods and parameters to achieve desiredtradeoffs between artifact visibility and rendering speed.

A visual image quality metric provides a quantitative qualitymeasurement. The perception-based metric is computed from a visualdiscrimination or human perception model, which is based on responses ofthe primary physiological mechanisms in the human visual system. Theoutput metric is a prediction of the visibility of image characteristicsor of differences between images. This metric has been found tocorrelate well with human perception, whereas standard engineeringmetrics, such as mean-squared error, consider only the differences indigital image values at individual pixels without regard to factors inimage display and perception that affect the visibility of thosedifferences. Mean-squared error is a quantity computed from differencesin image pixel values. The mean-squared error formula does not take intoaccount any factors that influence the ability of human observers todetect those differences. Images of the same object may have the samemean-squared error even though very visually different. A process or acombined measurement of various modeled neural processes may be modeledfor perception-based metrics. Perception-based metrics may includefactors such as luminance sensitivity, contrast sensitivity, selectiveresponses of spatial frequency, feature orientation, and/orpsychophysical masking. The visibility of image features or differencesbetween images may be measured quantitatively in standard psychophysicalunits of just-noticeable differences (JND). JND may be establishedthrough experimentation, set based on one users perception, or othertechnique. Other units of measurement may be used.

In the application for single-image features, JND can be measuredbetween a uniform background image and the target image for comparison.For paired images, JND reflects the perceived image differences betweenthe two images. Two-dimensional JND maps are generated for each spatialfrequency and orientation channel and can be combined across channels tocreate composite JND maps and across pixel locations to generate scalarJND values. VIQM values are linearly correlated with subjective qualityratings and task performance, and may provide a more reliable,quantitative measurement of what a human observer will actually perceivein image.

VIQM is used to evaluate quantitatively the visibility of volumerendered image artifacts. The amount of shading edge noise is quantifiedby measuring the responses of higher spatial frequency visual channelsto noise in single images. The visibility of non-smooth clip edges orother linear artifacts is quantified by measuring changes in themagnitude and angular distribution of responses in spatial frequencychannels to edges, striations, and other linear structures. The amountof striation artifacts without extended linear segments is quantified bymeasuring the changes in the magnitude and frequency distribution ofspatial frequency channel responses, such as for wood grain artifacts.The amount of view-dependent artifacts, such as opacity inconsistencies,is quantified by JND values across rendering pairs from differentrendered views.

FIG. 1 shows a system for artifact quantification in volume rendering.The system includes a processor 12, a memory 14, a display 16, and auser input 18. Additional, different, or fewer components may beprovided. For example, a network or network connection is provided, suchas for networking with a medical imaging network or data archivalsystem.

The system is part of a medical imaging system, such as a diagnostic ortherapy ultrasound, x-ray, computed tomography, magnetic resonance,positron emission, or other system. Alternatively, the system is part ofan archival and/or image processing system, such as associated with amedical records database workstation or networked imaging system. Inother embodiments, the system is a personal computer, such as desktop orlaptop, a workstation, a server, a network, or combinations thereof forrendering three-dimensional representations. For example, the system ispart of a developer's computer system for designing or calibrating arendering engine. As another example, the system is an end-user systemfor rendering images for diagnosis.

The user input 18 is a keyboard, trackball, mouse, joystick, touchscreen, knobs, buttons, sliders, touch pad, combinations thereof, orother now known or later developed user input device. The user input 18generates signals in response to user action, such as user pressing of abutton.

The user input 18 operates in conjunction with a user interface forcontext based user input. Based on a display, the user selects with theuser input 18 one or more controls, rendering parameters, values,quality metrics, an imaging quality, or other information. For example,the user positions an indicator within a range of available qualitylevels. In alternative embodiments, the processor 12 selects orotherwise controls without user input (automatically) or with userconfirmation or some input (semi-automatically).

The memory 14 is a graphics processing memory, video random accessmemory, random access memory, system memory, cache memory, hard drive,optical media, magnetic media, flash drive, buffer, combinationsthereof, or other now known or later developed memory device for storingdata or video information. The memory 14 stores one or more datasetsrepresenting a three-dimensional volume for rendering.

Any type of data may be used for volume rendering, such as medical imagedata (e.g., ultrasound, x-ray, computed tomography, magnetic resonance,or positron emission). The rendering is from data distributed in anevenly spaced three-dimensional grid, but may be from data in otherformats (e.g., rendering from scan data free of conversion to aCartesian coordinate format or scan data including data both in aCartesian coordinate format and acquisition format). The data is voxeldata of different volume locations in a volume. The voxels are the samesize and shape within the dataset. Voxels with different sizes, shapes,or numbers along one dimension as compared to another dimension may beincluded in a same dataset, such as is associated with anisotropicmedical imaging data. The dataset includes an indication of the spatialpositions represented by each voxel.

The dataset is provided in real-time with acquisition. For example, thedataset is generated by medical imaging of a patient. The memory 14stores the data temporarily for processing. Alternatively, the datasetis stored from a previously performed scan. In other embodiments, thedataset is generated from memory, such as associated with rendering avirtual object or scene. For example, the dataset is an artificial or“phantom” dataset. The dataset is designed, selected, or generated tohave desired characteristics, such as a representing a uniform sphere orspecific amount of noise. Different types of artifacts may use differentdatasets to define the artifact region and calibrate the measuredoutcome.

The processor 12 is a central processing unit, control processor,application specific integrated circuit, general processor, fieldprogrammable gate array, analog circuit, digital circuit, graphicsprocessing unit, graphics chip, graphics accelerator, accelerator card,combinations thereof, or other now known or later developed device forrendering. The processor 12 is a single device or multiple devicesoperating in serial, parallel, or separately. The processor 12 may be amain processor of a computer, such as a laptop or desktop computer, maybe a processor for handling some tasks in a larger system, such as in animaging system, or may be a processor designed specifically forrendering. In one embodiment, the processor 12 is, at least in part, apersonal computer graphics accelerator card or components, such asmanufactured by nVidia, ATI, or Matrox.

Different platforms may have the same or different processor 12 andassociated hardware for volume rendering. Different platforms includedifferent imaging systems, an imaging system and a computer orworkstation, or other combinations of different devices. The same ordifferent platforms may implement the same or different algorithms forrendering. For example, an imaging workstation or server implements amore complex rendering algorithm than a personal computer. The algorithmmay be more complex by including additional or more computationallyexpensive rendering parameters.

The processor 12 is operable to volume render a two-dimensionalrepresentation of the volume from the dataset. The two-dimensionalrepresentation represents the volume from a given or selected viewinglocation. Volume rendering is used in a general sense of rendering arepresentation from data representing a volume. For example, the volumerendering is projection or surface rendering.

The rendering algorithm may be executed efficiently by a graphicsprocessing unit. The processor 12 may be hardware devices foraccelerating volume rendering processes, such as using applicationprogramming interfaces for three-dimensional texture mapping. ExampleAPIs include OpenGL and DirectX, but other APIs may be used independentof or with the processor 12. The processor 12 is operable for volumerendering based on the API or an application controlling the API. Theprocessor 12 is operable to texture map with alpha blending, minimumprojection, maximum projection, surface rendering, or other volumerendering of the data. Other types of volume rendering, such asray-casting, may be used.

The rendering algorithm renders as a function of rendering parameters.Some example rendering parameters include voxel word size, sampling rate(e.g., selecting samples as part of rendering), interpolation function,size of representation, pre/post classification, classificationfunction, sampling variation (e.g., sampling rate being greater orlesser as a function of location), downsizing of volume (e.g., downsampling data prior to rendering), shading, opacity, minimum valueselection, maximum value selection, thresholds, weighting of data orvolumes, or any other now known or later developed parameter forrendering. The rendering parameters are associated with two or moreoptions, such as a range of possible fractional or integer values. Forexample, pre/post classification (classification timing) may be a binarysetting providing for mapping luminance to color before or afterinterpolation. The algorithm may operate with all or any sub-set ofrendering parameters. The rendering parameters may be set for a givenalgorithm, such as a renderer operating only with pre-classification.Other rendering parameters may be selectable by the developer orend-user, such as selecting sampling rate and word size by a developeror selecting shading options by an end-user.

The image is rendered from color data. Alternatively, the image isrendered from grayscale information. The visibility of volume renderingartifacts may be best shown by color information, grayscale information,or both. Since grayscale values are directly related to the luminanceoutput of an image display device, grayscale values may more likelyprovide visible artifacts. Pixel values for RGB(A) images can betransformed to grayscale values by applying standard conversions tohue-saturation-value (HSV) or NTSC luminance-chrominance (YUV)coordinates and setting the hue and saturation components to zero.Restricting the VIQM computation to the grayscale component of colorimages may simplify and expedite calculation without significant loss ofaccuracy for the volume rendering artifacts described herein.

The processor 12 is operable to determine a quantity representing anartifact. The two-dimensional representation of the volume alone or incombination with a reference image is used for the calculation. Thequantity is a function of a perception-based visual quality metric. Themetric correlates with human perceptual ratings, so is more reliable asa quantitative measurement of what would be perceived in an image by ahuman observer. Any visual model may be used. Example perception-basedvisual quality features contributing to the metric include verticalfeatures, horizontal features, other orientation/angle features,contrast sensitivity, luminance sensitivity, and/or psychophysicalmasking.

The selection of features is adapted based on use cases and can be acombination of features. The same features may be used for differentartifacts, but different features may be determined for differentartifacts. The feature set is based on the visual discrimination modelsimulation.

To compute the features in one example embodiment, the input image isfiltered by a set of biologically inspired spatial frequency andorientation tuned filters, defined mathematically as two-dimensionalGabor functions with various scales and orientations, breaking the imageinto 20 channels, at 5 different spatial frequencies (octave spacingfrom 0.5 cycles per degree to Nyquist/2) and 4 orientations (0, 45, 90,135 degrees). The filtering is done by fast convolution, whichtransforms the image into the frequency domain using the Fast-Fouriertransform (FFT) then point-by-point multiplication with the respectivefilter. Each channel is returned to the spatial domain by inverse FFT,with the complex values converted to real by taking the absolute value.Each channel is converted to local-contrast by dividing the pixelluminance by the local mean luminance. The local mean luminance iscomputed by fast convolution with a low-pass filter, whose pass-band istwo octaves lower than the channel's peak band-pass frequency.

The spatial frequency channels are weighted by a psychophysicallymeasured contrast sensitivity function, where sensitivity varies withspatial frequency and luminance. Any contrast sensitivity function maybe used. The contrast sensitivity function is a frequency-dependentfunction to be applied in each channel to adjust the sensitivities tomatch experimental psychophysical data. In general, the contrastsensitivity function has a peak in sensitivity around 4 cycles perdegree with monotonic decreases in sensitivity below and above the peak.The magnitude and shape of the curve depends on the light adaptationlevel of the eyes. The contrast sensitivity function depends onluminance and frequency. For example, the mean luminance of a givenimage is used to interpolate between curves, such as shown in FIG. 3.The contrast threshold shown is inversely related to sensitivity, so thecurves have minima instead of peaks.

One set of 20 channels representing the responses of the visual systemto luminance contrast is provided. Other numbers of channels, factors,groupings of features, divisions of spatial frequencies, and/ororientations may be used.

The metric is calculated from the features. Alternatively, data fromeach channel or combinations of channels may be used as a metric.

The data may be separated by spatial frequency, such as determiningquality metric values for data of the dataset at higher and lowerfrequencies. The dataset is low pass and high pass filtered. The qualitymetrics are then determined from the two different filter outputs. Bandpass or other spatial frequency isolation techniques may be used, suchas to create three or more output datasets at three or more respectivespatial frequencies.

The visual image quality metric is a two-dimensional map, linear map, orscalar measurement. For example, the metric is calculated for each pixelor groups of pixels for an image. Metric values as a function oftwo-dimensional distribution are provided and may be displayed as animage or contour map. In one embodiment, the metric values are providedas the two-dimensional channel or feature data, or combinations ofmultiple channels or features. The values of the quality metric may becombined or originally calculated along one or more lines for a linearmap. For a scalar value, an average, mean, median, highest, lowest, orother function is used to calculate the metric from the map.Alternatively, the calculation outputs a scalar value. By applyingpsychophysically measured weighting functions, including contrastsensitivity and masking, the visual image quality metrics are defined inJND units.

The scalar value may be for an entire image or one or more regions of animage. For example, selecting a higher or lowest value identifies aregion. As another example, a region of a pre-determined size, userselected region, or automatically determined region is used. The regionis centered on or otherwise placed to cover desired values of thechannel map, such as the highest value. The region is circular, square,rectangular, irregular, or other shape, such as following an edgefeature. A threshold may be applied to identify a plurality of regionswith sufficiently high or low values or to remove regions associatedwith very low or very high values. In one embodiment, the scalar valueis determined by the combination of mapped quality values within theregion or regions. In another example, segmentation or masking isperformed to remove areas that are irrelevant to the user (e.g., regionsoutside the imaged body).

One quality metric is used. Alternatively, more than one quality metricmay be calculated. A plurality of quality metrics may be combined as onevalue. Alternatively, each quality metric is calculated separately.

In one embodiment, the values for the channels are combined to from amap (e.g., two-dimensional distribution) or a scalar value (e.g., singlevalue of the metric for the image) as the metric. For example,two-dimensional maps are generated for each visual channel and thencombined across channels to create a composite map. Composite maps aregenerated by applying a maximum operation, Minkowski summation, or othercombination function at each pixel location across the selected set ofchannels. Scalar metrics are then determined for the composite map bycomputing statistical measures, such as the mean and standard deviationof the quality metric values, or finding histogram values (e.g., themedian or a high percentile (e.g., 90-99^(th)) value). As anotherexample, scalar values are determined for each channel map. The scalarvalues may be combined. Data from the map and/or the scalar values maybe used as the metric (e.g., VIQM).

The channels, functions, combination, spatial frequency, or other factorfor perception-based visual quality metrics used for a given rendering,rendering algorithm, or rendering engine may be based on theapplication. For a particular defined end user task, the choice of thescalar measurements are fine tuned to artifacts that are most importantto the task at hand. Individual frequency or orientation channels,composite maps, or other information that most reflect the salientartifacts are used for the application. The other channels are also usedor not used.

For example, each of the 20 channels above is used to quantify differenttypes of artifacts, but with different patterns or weighting used fordifferent artifacts. Any artifact may be identified and quantified, suchas shading noise, edge non-smoothness (e.g., striation), opacityinconsistency, or combinations thereof. The processor 12 identifies anartifact level or quantity for one or more of the artifact types.

In one embodiment, shading noise is quantified. A VIQM measurement ofthe amount of shading edge noise produced by a particular volumerendering engine is calculated. An image is rendered from artificialdataset or a real dataset with a known or specified amount of noise. Byusing a standardized phantom or dataset with a calibrated amount ofnoise, the measured responses of the higher spatial frequencies in thevisual channels can be compared with each other. The choice of the addednoise can be modeled after the typical noise in realistic data.Gaussian, stochastic, or other noise may be a simple noise that can beused as an indicative test. Stochastic noise in medical datasets isnormally composed of spatial frequencies that are relatively highcompared to the dominant frequencies found in anatomical structures.

One or more channels or perception-based visual quality metrics aredetermined from the rendered image. The perception-based visual qualitymetric used to identify shading noise is the higher spatial frequencyresponses of the two-dimensional representation. The higher or highestspatial frequency channel responses or features are calculated, and/or adifference between higher and lower spatial frequency channels iscalculated. The visibility of noise can be measured by the JND levels inthe higher spatial frequency channels, typically at 8 cycles per degreeor higher. The 8 cycles per degree is a measure of visual arc. Atdifferent distances, a given pixel represents a different degree of arc.Further away provides for a smaller arc, providing higher visual spatialfrequency.

Since shading edge noise varies between images and noise-free referenceimages are generally not available, measurements of noise visibilitywith VIQM are normally done using visual channels computed for a singleimage instead of paired images. The effects of rendering methods thatseek to reduce shading edge noise, for example, can be assessed andoptimized by evaluating the JNDs within high-frequency channels and inimage regions where the shading edge noise is visible. The image regionsare selected manually by the user or may be automatically detected, suchas associated with the maximum values of the high spatial frequencychannels. Lower JND levels in this case would indicate reduced noisevisibility. Other channels or calculations may be used.

Since shading edge noise is generally anisotropic and exhibits nopreferred orientation, VIQM computations can be simplified by firstcombining the orientation channels for a single frequency band. Anycombination may be used, such as a maximum or Minkowski distanceoperation at each pixel before computing scalar JND values for thecomposite map or one or more regions. Alternatively, one orientation isused, and the data for others is not used.

In one embodiment, edge non-smoothness is quantified. A real phantomcube or artificial dataset is rendered in an obliquely clipped view. Theedge non-smoothness is quantified by measuring the oriented responses ofchannels within the clipped region. The responses at a respectiveplurality of orientations relative to the two-dimensional representationare used as perception-based visual quality metrics. The responses oforientation channels in VIQM modeling are strongest when the channelorientation is aligned with linear structures or edges in an image.Consequently, the visibility of edges, striations, or other linearartifacts can be measured most sensitively by analyzing JND values inorientation channels that are most closely aligned with thosestructures. The magnitude of the oriented channel responses decreases asthe corresponding image structures become less visible. For example, areduction in edge sharpness due to a change in interpolation method maybe measured by the decrease in responses of the orientation channelsaligned with the edge, primarily in the higher spatial frequencies of 8cycles per degree or higher. A loss of edge smoothness due to stepartifacts decreases the response of channels aligned with the edge,again primarily in higher spatial frequency channels, but also increasesthe responses of channels aligned with the edges of the steps. Forexample, steps appearing along an edge tilted 450 from the horizontaldirection increase the JND output of orientation channels that respondstrongest to horizontal and vertical edges. Other channels orcalculations may be used.

The changes in or difference between channel responses are measuredusing single-image calculations. For example, an absolute quantity orscalar identifies the level of artifact. In other embodiments, apaired-image calculation is performed. The difference in responsebetween a reference image with relatively low artifact visibility andthe rendered image is determined.

For wood grain and other structural artifacts that have curvilinearfeatures without extended linear segments or constant orientation, themagnitude and distribution of channel responses across spatial frequencybands may be used to measure artifact visibility. Rendering methods orparameters that reduce the visibility of this type of artifact generallydecrease the response of channels across all frequency bands, but to agreater extent in the mid to high frequency bands (24 cycles perdegree), shifting the response distribution toward lower frequencies.The metric or metrics may be determined by magnitude and/or spatialdistribution from the orientation channels at the mid and/or highfrequency bands.

In another embodiment, opacity inconsistency is quantified. A pluralityof measures of differences between the two-dimensional representationand another two-dimensional representation of the volume rendered from adifferent perspective are used as the perception-based visual qualitymetrics. Opacity inconsistency is a view-dependent artifact. Opacityinconsistency or other view dependent artifacts may result frominadequate correction of various voxel sizes. To detect and quantifythis artifact, two or more images of an anisotropic volume of aspherical object are rendered at various viewing angles. Since thephantom object in this case is a sphere, there should not be imageregistration issues between these various views. The rendering isperformed with a translucent transfer function for opacityinconsistency. JND values are measured between combinations of imagepairs obtained from different rendering directions. The JND values areprovided by determining the differences between channel data, such asdifferences for each channel or between combinations of all or somechannels. The values represent differences between the renderings of thesame object from different directions, indicating visual opacityinconsistency.

Other types of artifacts may be quantified. The nature of humanperception is modeled to quantify the artifact. The contrast,orientation, spatial frequency, and/or other characteristic metric areused to quantify the artifact.

The quantity is determined from the channel data or comparison ofchannel data. For example, a pattern within or across channels is usedfor quantification. Any pattern may be used. For example, low frequencychannels are ignored. As another example, all of the channels are used,with certain channels weighted higher, certain channels combined toprovide one map or value, or certain channels relationship to otherchannels being used to identify the signature of a type of artifact.

The quantity may be a maximum value, average value or other valuecalculated from the just-noticeable differences or perception-basedmetric. For example, averages for regions associated with the highestone or more values are calculated from the two-dimensional map or imageof one or more channels. As another example, the maximum value isidentified for the entire image or separate sub regions.

In one embodiment, the quantity representing the level of artifact is afunction of a histogram of the perception-based visual quality metric.The histogram is populated from single pixels or from differentsub-regions of the channel or metric data. For sub regions, the metricdata is a two-dimensional map created by filtering the renderedrepresentation. The data is used to determine sub region scalar valuesor pixel values. The visibility (quantification) of rendering artifactsmay be represented by scalar metrics derived from the histogram of JNDvalues in the VIQM channel maps. Cases with extreme JND values(outliers) may distort the computed mean or region maximum value buthave little effect on the median value. The median may be a more stableindicator of overall artifact visibility and correlate with subjectivequality assessments. For applications in which an upper limit to thevisibility of artifacts is to be specified, it is advantageous tocompute a high-percentile JND value, typically greater than or equal tothe 90^(th) percentile, from the histogram. The value associated withthe higher percentile of the histogram distribution may ensure thatthere are no significantly large regions of an image for which the JNDvalues are unacceptably high.

Visual quality metric values are computed using all of the pixels of therendered image or image pair. Prior to determining or as part ofquantifying an artifact, the dataset may be masked. Many medical images,including those produced by volume rendering, include regions of littleor no diagnostic value. These regions may contain, for example, airspaces outside or inside the body. When these regions of an image areincluded in VIQM calculations, the data for the regions may distort thevalues of statistical and histogram-based scalar metrics and cause thequantity to depend on irrelevant image characteristics, such as theoverall pixel dimensions or field of view.

A binary image mask that excludes irrelevant regions of the image may beapplied to the dataset before rendering or to the visual channel mapsbefore computing a scalar quantity. Data associated with regions otherthan the object of interest may be removed, such as by segmentation orotherwise masked. Where an artificial dataset is provided, the datasetmay include zeros or other values representing masking, or there is noneed for masking. In the case of measuring artifact visual responses ona designed phantom, the region of interest can be pre-defined to theregion where the artifacts exist, such as along a clipped edge to avoiddistortion in the result VIQM metrics. For artificially generateddatasets with added noise or for datasets generated by scanning, datafrom regions outside an object of interest may be removed or set toanother value for masking.

Any masking function may be used, such as manual designation. Onemasking function is low pass filtering the dataset and applying athreshold. Data below the threshold is set to zero or removed. In oneembodiment, the dataset is masked as a function of at least theperception-based visual quality metric. One or more metrics are computedover sub regions of an image. For example, all twenty channels or justone channel (e.g., lowest frequency channel) are used. For multiplechannels, the data for each spatial location is combined, such asaveraging, maximum selection, or other combination. Background regionsare excluded by eliminating locations at which the channel map valuesfall below a given threshold, such as below a value of 0.1 JND given a0-1 range of values. JND values are normalized and are not imagedependent. This thresholded sub region method generates useful scalarmetrics in cases where the artifacts are highly localized and,consequently, the median and mean JND values would be grossly distortedby large numbers of insignificantly small values, if a JND threshold wasnot applied. The mask is applied to the dataset and another imagerendered for quantification, and/or the mask is applied to the separatechannels prior to determining a scalar quantity. Different or the samemask may be used for different channels.

The quantity representing the level of artifact may be used in any way,such as disclosed in U.S. published application Ser. No. ______(Attorney Reference No. 2006P14783US01), the disclosure of which isincorporated herein by reference. The rendering is performed as afunction of the perception-based visual quality metric in development,calibration, or real-time usage. For example, a user selects renderingparameters to be included, possible rendering parameter settings, groupsof settings, or other setting of a rendering algorithm based on themetric. The parameters (e.g., type of rendering) and/or parameter valuesassociated with noticeable differences or just noticeable differencesbased on the metric are used. At least one rendering parameter isaltered as a function of the artifact quantity. For example, the samplesize, sampling rate, classification, sampling variation, volume size,rendering method, or combinations thereof provide noticeable transitionsin artifact level.

The quantitative feedback allows more optimal design to balancerendering speed or other performance with imaging results based on theperception of the user. Parameters or settings providing insufficient orno improvement in perception of artifacts may be avoided to minimizeuser confusion or frustration. Settings associated with lesser artifactsmay be selected or determined.

As another example, different rendering algorithms and/or platforms arecalibrated. The visual quality metric values are made the same orsimilar for a given situation, allowing more consistent use across thedifferences. Transitions between user selectable settings may becalibrated to provide noticeable differences in artifact level. Thequality metric quantities allow developers to provide consistentlyrendering performance adjustments that relate to visible artifacts,rather than just rendering speed.

The perception-based visual quality metric is determined as a value fora given image, such as a volume rendered image. The difference betweenthe values for different images may be compared. For example, adifference of values for the same perception-based visual quality metricbetween two different rendered images is calculated. The perceptualdifferences between different settings, algorithms, platforms, or otherrendering factors are quantitatively represented by the difference. Thedifference may be calculated as a mathematical difference, a ratio, apercentage, or other function.

In one embodiment, the quality metric is calculated to indicate adifference from two or more images. The difference provides a visualimage quality metric-based quantitative quality index. For example, oneimage is used as a frame of reference. The visual image quality metricrelative to the frame or image of reference provides an index of thequality of a rendered image. The reference image may be at any qualitylevel. For example, the scalar value or values between a particularrendered image and the reference image are calculated. In the case of asingle volume rendering engine, the reference image may be the bestimage that this engine can produce with the highest resolutionparameters. Each rendered image from various combinations of parametersis mapped to scalar quality values based on the magnitude of qualitymetric values between the current image and the reference image. Thereference may be a lowest or other resolution image. The differences maybe mapped to integer levels, negative values, and/or fractional levels.

Different metrics or quantities may be provided for each type ofartifact. Alternatively, only one type of artifact is quantified. Inanother alternative, quantities for different types of artifacts arecombined to provide an overall artifact level, such as by averaging.

The display 16 is a monitor, LCD, projector, plasma display, CRT,printer, or other now known or later developed devise for outputtingvisual information. The display 16 receives images, quality metricvalues, or other information from the processor 12. The receivedinformation is provided to the user by the display 16.

For example, the display 16 displays the two-dimensional representationof the volume. Where a setting of the rendering is selected as afunction of the perception-based visual quality metric, the image mayhave an artifact less visually perceptible than for another setting. Twoimages rendered with different rendering settings have different levelsof visual artifacts, avoiding iterative adjustments having little or novisual difference for the end user. As another example, the justnoticeable differences, visual quality metric, or other quantificationbased on a visual model is displayed. The user may more objectivelycompare rendered images or determine a quality of a single renderedimage for any purpose using the quantity.

The display 16 is part of a user interface. The user interface is for adeveloper or end-user. For a developer, the user interface may includeone or more selectable quality metrics and output calculated values fora quality metric of a given image or between two images. The userinterface for perception based quantification may be integrated with orseparate from the volume rendering interface where the developer selectsdifferent rendering settings (e.g., parameters, values for parameters,and/or techniques). For an end user, the user interface may provideselectable levels of rendering where each level is associated with aperceptibly different visual artifact, limiting or avoiding unnecessaryrendering adjustments.

The memory 14 and/or another memory stores instructions for operatingthe processor 12. The instructions are for artifact quantification involume rendering. The instructions for implementing the processes,methods, and/or techniques discussed herein are provided oncomputer-readable storage media or memories, such as a cache, buffer,RAM, removable media, hard drive or other computer readable storagemedia. Computer readable storage media include various types of volatileand nonvolatile storage media. The functions, acts or tasks illustratedin the figures or described herein are executed in response to one ormore sets of instructions stored in or on computer readable storagemedia. The functions, acts or tasks are independent of the particulartype of instructions set, storage media, processor or processingstrategy and may be performed by software, hardware, integratedcircuits, firmware, micro code and the like, operating alone, or incombination. Likewise, processing strategies may includemultiprocessing, multitasking, parallel processing, and the like.

In one embodiment, the instructions are stored on a removable mediadevice for reading by local or remote systems. In other embodiments, theinstructions are stored in a remote location for transfer through acomputer network or over telephone lines. In yet other embodiments, theinstructions are stored within a given computer, CPU, GPU or system.

The system of FIG. 1 or another system has various developmental,calibration, and/or end-user uses. In one embodiment, theperception-base visual quality metric is used as a methodology for thedevelopment of visual-quality-driven volume rendering. The volumerendering is developed for easier end-user use. For end-user use, theuser input 18 receives an input of a selectable level of visualperception of an image artifact or rendering speed. The processor 12maps the input to one or more settings of one or more renderingparameters. A level of artifact is responsive to the input of theselectable level. For developer use, different rendering parametersettings are selected. Groups of settings associated with differentqualities of a visual aspect associated with a given application areselected. The map of settings to visual quality level is created,providing steps in artifact level associated with a visual aspect of therendering artifact, rather than just resolution differences.

A visual image quality metric-based quantitative index of image qualityis used or provided to the user. The index provides for task-specificvisual quality driven volume rendering. Rather than making subjectiveheuristic decisions about quality by directly selecting differentsettings for rendering parameters, the rendering engine developer isempowered with a simple quantitative mapping between the level ofperceived image artifacts and the corresponding set of renderingalgorithm parameters. Volume rendering parameters are controlled basedon meaningful levels of artifact as perceived by an end user.

For example, if N images are produced from a rendering engine by varyingthe rendering parameters and each image is compared to a high-qualityreference image, the visual image quality metric can be computed foreach of the N images in a manner based on the level of one or moreartifacts. Settings associated with insufficient visual differences maybe discarded. Each of the resulting visual image quality metric valuesare plotted and mapped to a single user interface parameter with N or asub-set of possible values to control the level of image quality. Thedeveloper, in turn, maps the quality levels in this user interface tothe sets of rendering parameters that produced the N or selected sub-setof images. The artifact level in combination with the visibility ofdesired features may be used.

From the end-user perspective, the quality levels correspond toobservable artifacts and can be adjusted without any knowledge about theunderlying rendering algorithms. From a software component developmentpoint-of-view, this independence from algorithm-specific parameters maybe used to derive a standardized quality parameter control interface.The same control of quality levels may be provided in differentrendering algorithms, platforms, or engines. The user control may beeasily exchangeable between platform-specific volume renderingcomponents.

In another embodiment, the perception-base visual quality metric is usedas a calibration tool for quality uniformity across volume renderingengines (e.g., algorithms, hardware, and/or both). The processor 12assists calibration of different rendering images as a function of theperception-based visual quality metric. In practice, volume renderingengines are often deployed in various software and graphicshardware-based implementations. In some cases, the same softwareapplication is deployed with different volume rendering enginesdepending on the available platform. In these cases, the consistency ofvisual image quality across platforms is important. Measuring theuniformity of visual quality, however, is complicated by the fact thateach volume rendering engine on each platform is controlled by differentalgorithm-specific rendering parameters and there may be no commonreference image.

For example, test images are evaluated in all possible pairings(round-robin pairing) of rendered images produced by different renderingengines but with nominally the same quality settings. The resultingvisual image quality metrics measure the degree of dissimilarity acrossthe various engines and may be used to define a threshold or upper limitfor an acceptable level of dissimilarity. If the level of measuredquality metric value is above a desired threshold, the renderingparameters of one or both of the rendering engines are adjusted with thegoal of achieving a better match in visual equivalency. This calibrationprocess is repeated between each pair of volume rendering engines sothat the visually noticeable differences for corresponding qualitylevels are below an acceptable threshold of difference. Absolute valuesor difference quantities may be used.

In another embodiment, the perception-base visual quality metric is usedas a calibration tool for controlling visual transitions between qualitylevels. The calibration is for different quality levels using a samerendering engine. Volume rendering engines may produce images usingseveral predetermined quality settings or levels that affect thetradeoff between visual quality and rendering speed. From the end-userperspective, it is desirable for the increments between quality levelsto be visually equal or similar to make the transition from low to highquality as smooth as possible. The visual magnitude of each quality stepis determined by computing visual image quality metric values for eachpair of consecutive images in a sorted sequence of quality levels.

The processor 12 renders with settings or groups of settingscorresponding to at least a threshold difference in the value of aperception-based visual quality metric. For example, a sequence ofimages for the respective quality levels is rendered. The qualitydifference between images as a function of the perception-based visualquality metric is determined. The difference is between adjacent pairsof images in one embodiment. For each consecutive pair, one of theimages is a reference image. Since consecutive pairs of reference andtest images overlap in this scheme, a “sliding reference” image is used.The magnitude of each visual increment is measured and the variationplotted as a function of quality level. Rendering parameters may beadjusted to control the visual increments between quality levels andachieve the desired uniformity. If any visual increments fall below adeveloper-selected threshold, the design of the volume rendering enginemay be simplified by retaining only the fastest renderer in each groupof visually equivalent or similar quality settings.

In another embodiment, the perception-base visual quality metric is usedas a tool for making quality versus speed performance decisions. Theoptions available in a rendering algorithm or platform may be selectedin a structured and objective way. The memory 14 stores groups ofsettings. Each group includes settings for a plurality of renderingparameters. Different rendering parameters may be provided as settingsin different groups. Each group is associated with different qualitylevels. The quality levels are determined as a function of theperception-based visual quality metric. The settings within each groupare further determined as a function rendering speed. For a givenquality level, the settings with the greatest rendering speed areselected.

The visual image quality metric is used for evaluating quality and speedperformance tradeoffs. For example, in certain volume renderingconditions, such as when the composited view is rendered from a verythick volume, the volume data is composited in such a way that littledifference is perceived between rendering using a slower buttheoretically more accurate method and rendering using a faster buttheoretically less accurate method. The conditions under which thisdifference is “small enough” such that using the faster method isjustifiable can be established using the perception-based metrics. Whenthe difference in values of the perception-based visual quality metricbetween images rendered using the faster and slower method is below acertain threshold, the faster method is to be used. The renderingsoftware or hardware is configured to provide the faster settings forthe desired quality level. The options available to a user may belimited or conveniently provided based on the rendering speed and thevisual aspect.

In another embodiment, the perception-base visual quality metric is usedas a runtime tool for dynamic adjustment of rendering parameters basedon actual data and system conditions. The processor 12 determines avalue for the perception-based visual quality metric for each ofmultiple images rendered with different settings. The processor 12selects settings as a function of the quality metric value and arendering performance difference between the different settings.Differences in datasets, such as size or spacing, and/or differences inavailability of rendering resources at a given time may result indifferent rendering speed or other performance. By determining thequality metric based on current datasets and conditions for two or moregroups of settings, one or more groups of settings may be selected asoptimal for current conditions. The current conditions are determinedduring runtime or are compared to previously determined ranges. Forpreviously determined ranges, a look-up table or thresholds are used toidentify settings appropriate for the current conditions.

This method of generating a quality verses performance tradeoff decisioncriterion may also be applied during development time. As an example foruse during runtime, the composited view is rendered from a dataset abovea certain thickness. The perceived difference between using differentinterpolation methods is very low for greater thicknesses. The renderingalgorithm applies a rule that when the thickness is above a threshold,then the faster rendering method is to be used. The perception-basevisual quality metric provides the developer or user an objective andsystematic tool to establish the quality and performance tradeoffcriterion with predictable quality consistency.

Other applications for development or rendering operation may be used.

FIG. 2 shows a method for artifact quantification in volume rendering.The method is implemented by the system of FIG. 1 or another system. Theacts of the method are performed in the order shown or other orders.Additional, different, or fewer acts may be provided. For example, act26 is optional.

A dataset for rendering is received with viewing parameters. The datasetis received from a memory, a scanner, or a transfer. The dataset isisotropic or anisotropic. The dataset has voxels spaced along threemajor axes or other format. The voxels have any shape and size, such asbeing smaller along one dimension as compared to another dimension.

The viewing parameters determine a view location. The view location is adirection relative to the volume from which a virtual viewer views thevolume. The view location defines a view direction and/or distance fromthe volume. The view location may be within the volume. The viewingparameters may also include scale, zoom, shading, lighting, and/or otherrendering parameters. User input or an algorithm defines the desiredviewer location.

Settings for rendering are also received. The settings are values forrendering parameters, selections of rendering parameters, selections oftype of rendering, or other settings. The settings are received as userinput, such as a developer inputting different settings for designing arendering engine. Alternatively or additionally, the settings aregenerated by a processor, such as a processor systematically changingsettings to determine performance and/or perception-based visual qualitymetric values associated with different settings. The settings may bepredetermined, such as provided in a look-up table. One, more or all thesettings may not be programmable.

In act 22, an image representation of a volume is volume rendered fromthe dataset representing the volume. Volume rendering is performed withthe dataset based on spatial locations within the sub-volume. Therendering application is an API, other application operating with anAPI, or other application for rendering.

Any now known or later developed volume rendering may be used. Forexample, projection or surface rendering is used. In projectionrendering, alpha blending, average, minimum, maximum, or other functionsmay provide data for the rendered image along each of a plurality of raylines or projections through the volume. Different parameters may beused for rendering. For example, the view direction determines theperspective relative to the volume for rendering. Diverging or parallelray lines may be used for projection. The transfer function forconverting luminance or other data into display values may varydepending on the type or desired qualities of the rendering. Samplingrate, sampling variation, irregular volume of interest, and/or clippingmay determine data to be used for rendering. Segmentation may determineanother portion of the volume to be or not to be rendered. Opacitysettings may determine the relative contribution of data. Otherrendering parameters, such as shading or light sourcing, may alterrelative contribution of one datum to other data. The rendering uses thedata representing a three-dimensional volume to generate atwo-dimensional representation of the volume.

The dataset for volume rendering is from any medical modality, such ascomputed tomography, magnetic resonance, or ultrasound. The dataset isfrom an actual scan. Alternatively, part or all of the dataset isartificial or modified. For example, a spherical phantom is volumerendered at a first viewing direction, and then volume rendered at asecond, different viewing direction.

In act 24, a processor predicts visibility to a user of one or moretypes of artifacts. Visibility to a user of an undesirable renderingfeature is quantified. One or more quantities of a visual perceptionmetric are calculated from the image representation. Just noticeabledifference levels of visibility of the undesirable rendering feature arecalculated. The scale may provide larger transitions between artifactlevels than “just noticeable.” Other units may be used. A human visualmodel is used to quantify from the image representation. Any step sizemay be used to represent transitions between levels of visibility ofartifacts.

The perception-based visual quality metric is calculated from a featureset of vertical features, horizontal features, other oriented features,contrast sensitivity, luminance sensitivity, psychophysical masking, orcombinations thereof. More than one quality metric may be calculatedfrom the feature set. For example, values for a plurality ofperception-based visual quality metrics are calculated, and the valuesare combined. Values for the metric or metrics may be calculated for oneor more spatial frequency bands of the data. The values are for pointlocations, regions, or the entire image. The quantity is, alternatively,a value from one of the features without further calculation.

The quality metric value or values are for a single renderedrepresentation. Alternatively, the quality metrics represent adifference between a plurality of rendered representations.

In one embodiment, the quantity is determined by correlating responsesfrom a plurality of perception-based visual quality metrics to renderingartifacts. For example, a greater response for higher spatial frequencyof two or more of the metrics than lower spatial frequency isidentified. The amount of difference or correlation characteristic isdetermined as the quantity. As another example, a greater response fororientation metrics is identified. The level of orientation orcorrelation characteristic across orientations channels as a function ofspace is determined as the quantity. In another example, a greaterresponse of one or more of the metrics at the first viewing directionthan the second viewing direction is identified. The difference betweenmetrics at the different viewing angles or other correlationcharacteristic is determined as the quantity.

In other embodiments or after correlation to identify a type orexistence of the artifact, a histogram is used to determine thequantity. The quantified visibility is a function of a histogram of oneor more perception-based visual quality metrics. The channel values forindividual pixels or scalars from pixel regions (e.g., sub-regions ofthe volume rendered image) populate the histogram. Separate histogramsmay be generated for different channels. Data from multiple channels maybe combined and used to populate a histogram. One channel may be usedafter identification using a plurality of channels. The median or otherhistogram characteristic may be used as the quantity. For example, the90-95% value of the histogram is used. In other embodiments, a histogramis not provided, such as averaging the channel data after applying asmoothing filter or without applying a smoothing filter. Any scalarcalculation may be used. In other alternative embodiments, the channeldata is displayed as an image. The modulation of intensity or color foreach pixel represents the quantity.

In act 26, one or more rendering artifacts are identified. Theidentification may be general, such as providing the quantification torepresent a level of artifact. The identification may be specific, suchas identifying one or more regions of the rendered image associated witha pattern, correlation, or sufficient quantity (e.g., level ofartifact). The identification is as a function of the quantity.

Any or multiple types of artifacts may be identified together orseparately. For example, shading noise, edge non-smoothness, and opacityinconsistencies are identified as separate artifacts from the renderedimage. The correlation or pattern of metrics and/or data from differentchannels identifies these different types of artifacts.

The quantity may be displayed or output for any use. For example, volumerendering is performed again using different settings where the artifactis sufficiently visible based on the quantity. The quantity from onerendered image may be compared with a quantity from another renderedimage to determine a more desirable calibration, algorithm, or settings.

While the invention has been described above by reference to variousembodiments, it should be understood that many changes and modificationscan be made without departing from the scope of the invention. It istherefore intended that the foregoing detailed description be regardedas illustrative rather than limiting, and that it be understood that itis the following claims, including all equivalents, that are intended todefine the spirit and scope of this invention.

1. A system for artifact quantification in volume rendering, the system comprising: a memory operable to store a dataset representing a three-dimensional volume; a processor operable to volume render a two-dimensional representation of the volume from the dataset, and operable to determine a quantity representing an artifact as a function of a perception-based visual quality metric; and a display operable to display the two-dimensional representation of the volume, the quantity, or both.
 2. The system of claim 1 wherein the perception-based visual quality metric is a function of vertical features, horizontal features, angle features, contrast sensitivity, luminance sensitivity, psychophysical masking, or combinations thereof.
 3. The system of claim 1 wherein the processor is operable to alter at least one rendering parameter as a function of the quantity, the at least one rendering parameter comprising sample size, sampling rate, classification, sampling variation, volume size, rendering method, or combinations thereof.
 4. The system of claim 1 wherein the artifact comprises shading noise, edge non-smoothness, opacity inconsistency, or combinations thereof.
 5. The system of claim 4 wherein the artifact comprises shading noise, and wherein the perception-based visual quality metric comprises higher spatial frequency response of the two-dimensional representation.
 6. The system of claim 4 wherein the artifact comprises edge non-smoothness, and wherein the perception-based visual quality metric comprises orientation responses at a respective plurality of orientations relative to the two-dimensional representation.
 7. The system of claim 4 wherein the artifact comprises opacity inconsistency and wherein the perception-based visual quality metric comprises a plurality of measures of differences between the two-dimensional representation and another two-dimensional representation of the volume rendered from a different perspective.
 8. The system of claim 4 wherein the perception-based visual quality metric is a function of vertical features, horizontal features, angle features, contrast sensitivity, luminance sensitivity, psychophysical masking, or combinations thereof; and wherein the processor is operable to identify, within the two-dimensional representation, shading noise, edge non-smoothness, and opacity inconsistency.
 9. The system of claim 1 wherein the processor is operable to mask the dataset as a function of at least the perception-based visual quality metric.
 10. The system of claim 1 wherein the quantity is a function of a histogram of the perception-based visual quality metric from different sub-regions of the two-dimensional representation.
 11. A method for artifact quantification in volume rendering, the method comprising: volume rendering a volume rendered image from a dataset; and quantifying, with a processor, visibility to a user of an undesirable rendering feature in the volume rendered image.
 12. The method of claim 11 wherein quantifying comprises calculating a perception-based visual quality metric as a function of vertical features, horizontal features, orientation features, contrast sensitivity, luminance sensitivity, psychophysical masking, or combinations thereof.
 13. The method of claim 11 wherein quantifying comprises correlating responses from a plurality of perception-based visual quality metrics to rendering artifacts.
 14. The method of claim 13 wherein correlating comprises identifying a greater response for higher spatial frequency of two or more of the metrics than lower spatial frequency; and further comprising: identifying shading noise, as a function of the correlation, as the rendering artifact.
 15. The method of claim 13 wherein correlating comprises identifying a greater response for orientation metrics; and further comprising: identifying edge non-smoothness, as a function of the correlation, as the rendering artifact.
 16. The method of claim 13 wherein volume rendering comprises volume rendering a spherical phantom at a first viewing direction, further comprising volume rendering the spherical phantom at a second, different viewing direction; wherein correlating comprises identifying a greater response of one or more of the metrics at the first viewing direction than the second viewing direction; and further comprising: identifying opacity inconsistency, as a function of the correlation, as the rendering artifact.
 17. The method of claim 11 wherein quantifying comprises calculating a just noticeable difference level of visibility of the undesirable rendering feature.
 18. The method of claim 11 wherein the quantified visibility is a function of a histogram of one or more perception-based visual quality metrics from different sub-regions of the volume rendered image.
 19. In a computer readable storage medium having stored therein data representing instructions executable by a programmed processor for artifact quantification in volume rendering, the storage medium comprising instructions for: volume rendering an image representation of a volume from a data set representing the volume; calculating a first quantity with a human visual model from the image representation; and identifying a rendering artifact as a function of the first quantity.
 20. The instructions of claim 19 wherein calculating comprises calculating as a function of two or more perception-based visual quality metrics each corresponding to one of vertical features, horizontal features, angle features, contrast sensitivity, luminance sensitivity, psychophysical masking, or combinations thereof; and wherein identifying comprises identifying, within the image representation, shading noise, edge non-smoothness, and opacity inconsistency. 